Here’s the full story:
I bought it 2 days ago, (couldn't find anything better), tested some games on it and tried YSmenu to run the games that it couldn’t run, here the 3ds freezes and I turn off the power, when I turn on the power again it shows the “turn off the power, check the manual” message.
Reading online I see that the Ysmenu isn’t compatible with the R4iTT NEW (…sigh...) so I find and follow these instructions:
Format the SD card with SD Formatter 3.1
Download and copy to the SD root the latest Kernal for the specific card
Download and copy to the SD root the firmware updater for the specific card
Then I insert the card into the DS Lite but it won’t read it, it shows the “Nintendo” logo in the upper screen and the “touch the screen to continue” message in the bottom screen (even when the card is inserted without the SD card) but when I press any button I get white screens and nothing happens.
I’m using the “fwUpdate_V5.05” firmware updater and the “New2.37_English” kernal from the card website (R4itt.net)I’ve read that some cards need an extra, working, card to do the upgrade but I don’t think this is the case for the R4iTT New… Anyway any help would be great!

1. Go to the official R4iTT new downloadpage
2. Select a language from the in the left column
3. Extract the Kernel with Winrar or 7zip
4. Copy the files in the archive at your MicroSD card
5. Repeat it with the Firmware upgrade
6. Remember to copy the fwUpdate....nds and the files of the Kernel archive (eg. the _DS_MENU.DAT and the SYSTEM folder) into the root of your card (no subfolders!)
7. Boot the card with your DS lite
8. Start the fwUpdate....nds
9. Wait until the process is finished (and maybe you have to confirm it with a button)
10. Start your R4 at the 3DS

I added those trying to find something that works. I think they are part of the "RetroGameFan Multi Cart Update v6.95".

I Formatted the SD card and followed your instructions (again) but I keep having the same problem:
when I insert the card into the DS Lite I press any button and nothing happens, both screens turn white.